Progressive Feedback For High Resolution Limited Feedback Wireless Communication

ABSTRACT

A system and method is proposed for progressively quantizing channel state information for application in a MIMO (multiple input multiple output) communication system. A method includes computing an estimate of a communications channel between a subscriber unit and a base station, quantizing the estimate with a first codebook, thereby producing a first quantized estimate, quantizing an (n−1)-th quantized estimate with an n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R, R is a total number of quantizations of the estimate, wherein the n-th codebook is a localized codebook. The method also includes incrementing n, repeating the quantizing an (n−1)-th quantized estimate until n=R, and transmitting information based on the R quantized estimates to the base station.

This application claims the benefit of U.S. Provisional Application No.61/049,694, filed on May 1, 2008, entitled “PROGRESSIVE FEEDBACK FORHIGH RESOLUTION LIMITED FEEDBACK WIRELESS COMMUNICATION,” whichapplication is hereby incorporated herein by reference

TECHNICAL FIELD

The present invention relates, in general, to wireless communicationssystems, and, in particular embodiments, to progressive feedback forhigh resolution limited feedback wireless communications.

BACKGROUND

Multiple-input multiple-output (MIMO) technology exploits the spatialcomponents of the wireless channel to provide capacity gain andincreased link robustness. After almost a decade of research,multiple-input multiple-output (MIMO) has finally been adopted inseveral standards including IEEE 802.16e-2005 and IEEE 802.11n; productsbased on draft standards are already shipping. MIMO is often combinedwith OFDM (orthogonal frequency division multiplexing), a type ofdigital modulation that makes it easy to equalize broadband channels.

In MIMO communication systems, at the transmitter, data are modulated,encoded, and mapped onto spatial signals, which are transmitted from themultiple transmit antennas. A main difference with non-MIMOcommunication systems is that there are many different spatialformatting modes for example beamforming, preceding, spatialmultiplexing, space-time coding, and limited feedback preceding, amongothers (see A. Paulraj, R. Nabar, and D. Gore, Introduction toSpace-Time Wireless Communications, 40 West 20th Street, New York, N.Y.,USA: Cambridge University Press, 2003). The spatial formattingtechniques have different performance (in terms of capacity, goodput,achievable rate, or bit error rate for example) in different channelenvironments. Consequently, there has been interest in adapting thespatial transmission mode based on information obtained about thechannel.

One especially effective technique is known as closed-loop MIMOcommunication, where channel state information or otherchannel-dependent information is provided from the receiver to thetransmitter through a feedback link. This information is used tocustomize the transmitted signal to the current propagation conditionsto improve capacity, increase diversity, reduce the deleterious effectsof fading, or support more users in the communication link for example.Because the bandwidth of the feedback link is low, techniques forquantizing channel state information and other receiver information havebecome increasingly important. This research area dealing withquantizing channel state information and other channel-dependentparameters is broadly known as limited feedback communication (see D. J.Love, R. W. Heath, Jr., W. Santipach, and M. L. Honig, “What is theValue of Limited Feedback for MIMO Channels?” IEEE CommunicationsMagazine, vol. 42, no. 10, pp. 54-59, October 2003). The concept oflimited feedback can be applied to any communication system but it isespecially valuable in MIMO communication systems.

Limited feedback precoding is a preferred embodiment of the limitedfeedback concept for MIMO communication channels. The main concept oflimited feedback precoding is that an index of a quantized precodingmatrix from a predetermined codebook of codewords in the form ofprecoding vectors or matrices (known at both the transmitter andreceiver), is determined at the receiver and sent back to thetransmitter over the feedback link. The determination of the preferredindex can be made based on several different design criteria includingmaximum capacity, maximum goodput, minimum error rate, or minimumdistortion for example. While the optimum index can be computed based onany number of measurements made at the receiver including the channelstate estimates and statistics of the channel state like the mean andcovariance, computations based directly on the channel state estimatesare known to have the best performance.

The codebook employed in a limited feedback technique is known to havean impact on the eventual system performance. Larger codebooks, whichrequire more bits to represent the index, are generally of higherresolution and have better performance at the expense of requiring morefeedback to send back the codebook index. Smaller codebooks requirefewer bits to represent the index of the chosen codeword, thus entailingreduced feedback overhead at the expense of lower resolution.Furthermore, larger codebooks require more storage space, which may taxthe storage capabilities of the transmitter and the receiver. Becausethe feedback channel constitutes system overhead, there is a tensionbetween using more feedback overhead to obtain higher resolution andusing less feedback to reduce the penalty due to feedback overhead.

Many different codebook designs have been proposed in the literature foruse in limited feedback precoding systems. A prominent example areGrassmannian codebooks (see D. Love and R. W. Heath Jr., “Limitedfeedback unitary precoding for orthogonal space-time block codes,” IEEETrans. Signal Processing, vol. 53, no. 1, pp. 64-73, 2005; D. Love, J.Heath, R. W., and T. Strohmer, “Grassmannian beamforming formultiple-input multiple-output wireless systems,” IEEE Trans. Inform.Theory, vol. 49, no. 10, pp. 2735-2747, 2003; and D. Love and J. Heath,R. W., “Limited feedback unitary precoding for spatial multiplexingsystems,” IEEE Trans. Inform. Theory, vol. 51, no. 8, pp. 2967-2976,2005). With Grassmannian codebooks, the codebook is designed tocorrespond to a good packing on the Grassmann manifold, essentiallymaximizing the minimum subspace distance measured using for example theChordal distance, Fubini-Study distance, and projection 2-norm distance.These codebooks are optimal in some sense but only exist in specialcases and are extremely difficult to compute even when they exist.

Vector quantization concepts have also been used to design codebooks(see A. Narula, M. J. Lopez, M. D. Trott, and G. W. Wornell, “Efficientuse of side information in multiple-antenna data transmission overfading channels,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp.1423-1436, October 1998; and J. C. Roh and B. D. Rao, “Transmitbeamforming in multiple-antenna systems with finite rate feedback: aVQ-based approach,” IEEE Trans. Inform. Theory, vol. 52, no. 3, pp.1101-1112, March 2006). The idea is that the codebook is constructedusing an iterative technique according to a distortion measure likesubspace distance, average capacity, or bit error rate for example. Thisapproach can be used to design a codebook of any size but the codebookusually lacks structure to allow efficient storage. Further suchcodebooks may not be globally optimal since an iterative algorithm isemployed.

Other codebooks have been proposed based on the Fourier transform (seefor example D. Love and R. W. Heath Jr., “Limited feedback unitaryprecoding for orthogonal space-time block codes,” IEEE Trans. SignalProcessing, vol. 53, no. 1, pp. 64-73, 2005; and R1-072235, Samsung,“Codebook design for 4tx SU MIMO,” 3GPP TSG RAN WG1 49, Kobe, Japan,7-11 May, 2007. Available at http://www.3gpp.org/ftp/tsg ran/WG1RL1/TSGR1 49/Docs/R1-072235.zip). These codebooks can be storedefficiently and have properties that may simplify computation. They onlyexist though for small codebook sizes.

Yet other codebooks have been designed based on Kerdock codes ormutually unbiased bases (T. Inoue and R. W. Heath Jr., “Kerdock codesfor limited feedback MIMO systems,” Mar. 30-Apr. 4, 2008, Proc. of theIEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Las Vegas,Nev.). This codebook is constructed from multiple sets of unitarymatrices such that the maximum minimum inner product between columns ismaximized. They have good properties that make them easy to search and aquarternary alphabet that makes them easy to store but the codebook sizeis limited.

Other codebooks have been suggested that have a nested structureallowing them to work with a different number of substreams includingone, two, three, and four streams. An example of this is the Householdercodebook design (R1-072201, “Way forward on 4-tx antenna codebook forsu-mimo,” 3GPP TSG RAN WG1 49, Kobe, Japan, 7-11 May, 2007. Available athttp://www.3gpp.org/ftp/tsg ran/WG1 RL1/TSGR1 49/Docs/R1-072201.zip)where a beamforming codebook like a Grassmannian codebook is to computeHouseholder reflection matrices that are used to construct more complexcodebooks using columns from these matrices. These codebooks have someadvantages that they can be easy to store since the coefficients of thecodewords can be represented with low precision, though the codebooksare somewhat small.

Other codebook designs have been suggested to exploit adaptive feedbackto reduce the amount of feedback. One approach is to take advantage ofspatial and temporal correlation to reduce the amount of feedbackrequired. For example one approach is to use a set of possiblecodebooks. The best codebook changes over time and is adaptively sentback to the transmitter (see for example B. Mondal and R. W. Heath, Jr.,“Channel Adaptive Quantization for Limited Feedback MIMO Beamformingsystems,” IEEE Trans. on Signal Processing, vol. 54, no. 12., pp.4741-4740, December 2006). This approach requires additional overhead tosignal the switch between codebooks in addition to the extra storagespace to store the set of possible codebooks. In another approach toadaptive feedback (B. C. Banister and J. R. Zeidler, “Feedback AssistedStochastic Gradient Adaptation of Multiantenna Transmission,” IEEETransactions on Wireless, vol. 4, no. 3, pp. 1121-1135, May 2005),gradients in an adaptive algorithm are quantized and sent back to thetransmitter. This algorithm may take a long time to converge.

Another approach for codebooks that facilitate adaptation uses alocalized codebook is combined with a non-local codebook to facilitateadaptation to spatial correlation (R. Samanta and R. W. Heath Jr.,“Codebook Adaptation for Quantized MIMO Beamforming Systems,” Proc. ofthe Asilomar Conference, October 2005, pp. pp. 376-380). This paperdescribes a localized codebook, scaling and rotation operations, and anadaptation mechanism. In this prior work localized codebooks aredescribed but are used only when the source distribution is determinedto be suitably localized. Thus there is an algorithm that effectivelychooses the base codebook and the optimum radius for the localizedcodebook, then that codebook used during several quantization periods.Design criteria for finding the localized codebooks were not discussed.Their application to multiuser communication was not mentioned.Similarly, this concept was used in reference V. Raghavan, R. W. Heath,and A. M. Sayeed, “Systematic Codebook Designs for Quantized Beamformingin Correlated MIMO Channels,” IEEE J. Select. Areas Commun., vol. 25,no. 7, pp. 1298-1310, September 2007. The key concept in this prior workis to show when correlated channels have sufficiently localizedeigenvectors that can be reasonably quantized with a localized codebook.Design criteria for finding the localized codebooks were not discussed.Their application to multiuser communication was not mentioned.

Yet other codebooks are designed so that they can be searchedefficiently (see for example D. J. Ryan, I. V. L. Clarkson, I. B.Collins, D. Guo, and M. L. Honig, “QAM Codebooks for Low-ComplexityLimited Feedback MIMO Beamforming,” Proc. of ICC 2007, pp. 4162-4167).In this case special mathematical structure in the codebook permitsalgorithms that can perform the quantization efficiently, at the expenseof a larger codebook size for the same performance with other codebooktechniques. The ability to search the codebook is especially importantfor high resolution limited feedback, which requires large codebooksizes, because without special structure a brute-force search of thecodebook is required.

High resolution, or larger, codebooks are especially important for atype of MIMO communication known as multiuser MIMO or MU-MIMO (see D.Gesbert, M. Kountouris, R. W. Heath, Jr., C. B. Chae, and T. Salzer,“From Single user to Multiuser Communications: Shifting the MIMOparadigm,” IEEE Signal Processing Magazine, Vol. 24, No. 5, pp. 36-46,October, 2007 and the references therein). In MU-MIMO, multiple usersshare the propagation channel. In what is known as the downlink orbroadcast MU-MIMO channel, information is sent to multiple users viaspecially designed transmit beamformers or precoders determined based onchannel state information. Users send information about their channelstate through an uplink feedback channel.

The concept of limited feedback has been used in MU-MIMO communicationsystems (see for example N. Jindal, MIMO Broadcast Channels with FiniteRate Feedback, IEEE Trans. Information Theory, Vol. 52, No. 11, pp.5045-5059, November 2006) to compress quantized information sent on theuplink. A main conclusion of this paper is that the codebook size in aMU-MIMO communication system measured in terms of number of bits growsin proportion to the number of users in the system. So if a single userMIMO system requires a 6 bit codebook, a MU-MIMO system supportingtransmission to two users might require at least a 12 bit codebook (64codewords versus 4,096 codewords). The codebook size also grows as afunction of the operating SNR due to an error floor effect. Schedulingthe best users can reduce this effect (see for example T. Yoo, N.Jindal, and A. Goldsmith, Multi-Antenna Downlink Channels with LimitedFeedback and User Selection, IEEE Journal Sel. Areas in Communications,Vol. 25, No. 7, pp. 1478-1491, September 2007). Nonetheless, MU-MIMOrequires high resolution limited feedback codebooks. Codebook designshave not been extensively investigated for MU-MIMO communicationsystems. The codebook designs discussed already are typically small,without the required resolution for MU-MIMO, or are large but requirehigh complexity to search.

Practical codebook design require that several criteria are met, whichis not solved. They should have low storage requirements. This meansthat high precision is not required to store each codebook entry.Unfortunately, much of the prior work (Grassmannian and vectorquantization codebooks for example) does not satisfy this criterion.

Efficient algorithms with reasonable computational complexity should beavailable to efficiently search for an optimum codeword in the codebook.Unfortunately, most prior work (with the exception of the work by D. J.Ryan et. al.) gives codebooks that do not facilitate especiallyefficient codeword search. Most existing approaches for limited feedbackcodebook design are single shot in that they quantize the currentchannel state without considering the previous channel state. Adaptivecodebook strategies, though, could be used to improve performance byonly compressing changes in the channel state. Special codebooks areneeded to allow efficient adaptive feedback but have only seen limiteddevelopment (the work by Samanta et. al. for example).

Finally, it would be advantageous if codebooks could be applied to bothsingle user and multiuser communication settings. Unfortunately, singleuser codebooks are usually designed to be smaller and are not big enoughto support the resolution required by multiuser codebooks.

SUMMARY OF THE INVENTION

Select ones of the various embodiments of the present invention betterquantize channel state information to achieve higher resolutionquantization and, therefore, better performance of a wireless system. Itprovides a system and method for progressively quantizing channel stateinformation using a non-localized base codebook and a localized codebookthat shrinks with each successive refinement of the quantization step.Using preferred embodiments, the localized quantization can be performedwith low storage and low complexity. Quantization with large codebookscan be performed by progressively applying the localized quantizationalgorithm, instead of performing a single shot quantization with asingle very large codebook.

Representative embodiments of the present invention provide a system forprogressive quantization in a wireless communication system with aplurality of base transceiver stations and a plurality of subscriberunits. The system employs progressive channel state quantization at thesubscriber and progressive channel reconstruction at the basetransceiver station. Quantized channel state information may be used tocompute the transmit beamforming vector for a single user or to computethe transmit beamforming vectors for serving multiple userssimultaneously. A base codebook and a localized codebook facilitate theprogressive quantization operation.

A method for progressive refinement channel state quantization isdescribed that comprises quantization using a base codebook, successivequantization refinement steps using a localized codebook with theeffective radius of the localized quantization operation getting smallerwith each codebook step. In a preferred embodiment the successivequantization refinement steps scale the localized codebook, rotate thescaled localized codebook, and quantize with the rotated and scaledcodebook. In another preferred embodiment the successive quantizationrefinement steps scale the localized codebook, rotate the channelobservation, and quantize with the rotated channel observation with thescaled codebook. In another preferred embodiment the successivequantization refinement steps scales the observed channel observation,rotates the scaled channel observation, then quantizes the rotated andscaled channel observation with the localized codebook.

A method for progressive reconstruction of a progressively quantizedchannel state is described that comprises extracting the base andrefinement codebook indices from a feedback message, scaling the entryof a localized codebook, rotating the scaled entry, and repeating theprocess.

In accordance with an embodiment, a method for subscriber unit operationin a wireless communications system is provided. The wirelesscommunications system having a base station. The method includescomputing an estimate of a communications channel between the subscriberunit and the base station, quantizing the estimate with a firstcodebook, thereby producing a first quantized estimate, quantizing an(n−1)-th quantized estimate with an n-th codebook, thereby producing ann-th quantized estimate, incrementing n, repeating the quantizing an(n−1)-th quantized estimate until n>R, and transmitting informationbased on the R quantized estimates to the base station. Where n is aninteger value ranging from 2 to R and n initially being equal to 2, R isa total number of quantizations of the estimate. The n-th codebook is alocalized codebook,

In accordance with another embodiment, a method for base stationoperation in a wireless communications system is provided. The methodincludes receiving channel information from a subscriber unit,extracting R codebook indices from the channel information,progressively reconstructing a channel estimate using the R codebookindices, and outputting the reconstructed channel estimate. Where R isan integer number. The reconstructing starts at a first codebook indexand continues to the R-th codebook index and the reconstructing achannel estimate using an n-th index makes use of an n-th codebook.

In accordance with another embodiment, a base station is provided. Thebase station includes a scheduler, a beamforming unit coupled to thescheduler, a progressive reconstruction unit, a single user unit coupledto the scheduler, to the beamforming unit, and to the progressivereconstruction unit, and a multi-user unit coupled to the scheduler, tothe beamforming unit, and to the progressive reconstruction unit. Thescheduler selects one or more users for transmission in a transmissionopportunity, the beamforming unit maps information for the selectedusers onto a beamforming vector for transmission, and the progressivereconstruction unit reconstructs a channel estimate from channelfeedback information provided by a subscriber station. The progressivereconstruction unit progressively creates the channel estimate from abase index to a base codebook and at least one refinement index to alocalized codebook. The base index and the refinement indices areconveyed in the channel feedback information. The single user unitprovides single user beamforming vectors to the beamforming unit. Thesingle user beamforming vectors are generated by the single user unitbased on the selected users and the channel estimate, and the multi-userunit provides multi-user beamforming vectors to the beamforming unit.The multi-user beamforming vectors are generated by the multi-user unitbased on the selected users and the channel estimate.

In accordance with another embodiment, a subscriber station is provided.The subscriber station includes a channel estimate unit coupled to areceive antenna, a mobility estimate unit coupled to the receiveantenna, a progressive quantization unit coupled to the channel estimateunit and to the mobility estimate unit, and a progressive feedback unitcoupled to the progressive quantization unit. The channel estimate unitestimates characteristics of a communications channel between thesubscriber station and a base station, and the mobility estimate unitcomputes a measure of the mobility of the subscriber station. Theprogressive quantization unit progressively quantizes the estimatedcharacteristics of the communications channel by quantizing theestimated characteristics with a base codebook, thereby producing aquantized estimated characteristics, and progressively quantizing thequantized estimated characteristics with localized codebooks. Theprogressive feedback unit generates a feedback message from indices of aresult of each of the quantizations into their respective codebooks.

An advantage of an embodiment is that a multiple codebooks are used toprovide a coarse quantization of the channel state followed byrefinements of the quantization of the channel state. The use ofmultiple codebooks may significantly reduce codebook size as well as theamount of feedback information.

Another advantage of an embodiment is that the number of refinements ofthe quantization may be adaptive. The number of refinements may be basedon factors such as mobile device mobility, desired performance, usertype, and so forth.

Yet another advantage of an embodiment is that incremental feedback maybe used. In incremental feedback only an index of a refinement of anearlier quantization is fedback instead of indices of an entirequantization.

A further advantage of an embodiment is that the progressive refinementis applicable to both single user and multiuser situations.

The foregoing has outlined rather broadly the features and technicaladvantages of the present invention in order that the detaileddescription of the embodiments that follow may be better understood.Additional features and advantages of the embodiments will be describedhereinafter which form the subject of the claims of the invention. Itshould be appreciated by those skilled in the art that the conceptionand specific embodiments disclosed may be readily utilized as a basisfor modifying or designing other structures or processes for carryingout the same purposes of the present invention. It should also berealized by those skilled in the art that such equivalent constructionsdo not depart from the spirit and scope of the invention as set forth inthe appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, and theadvantages thereof, reference is now made to the following descriptionstaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a diagram of a wireless communication system;

FIG. 2 a is a diagram of a prior art base transceiver station (BTS);

FIG. 2 b is a diagram of a prior art subscriber unit;

FIG. 3 a is a diagram of a BTS;

FIG. 3 b is a diagram of a subscriber unit;

FIG. 4 a is a diagram of a base codebook;

FIG. 4 b is a diagram of a localized codebook;

FIG. 5 a is an diagram of a localized codebook with concentric rings;

FIG. 5 b is an diagram of a localized codebook with concentric ringswith rotation;

FIG. 5 c is an diagram of a localized codebook with a disc;

FIG. 6 a is a diagram of quantization by a base codebook;

FIG. 6 b is a diagram of a first refinement quantization by a localizedcodebook;

FIG. 6 c is a diagram of a second refinement quantization by a localizedcodebook;

FIG. 7 a is a block diagram of a circuit for use in the generation of afeedback message;

FIG. 7 b is a block diagram of a circuit for use in the generation of afeedback message;

FIG. 8 a is flow chart of subscriber unit operations in the progressiverefinement of the quantization of channel state;

FIG. 8 b is flow chart of subscriber unit operations in the progressiverefinement of the quantization of channel state;

FIG. 8 c is flow chart of subscriber unit operations in the progressiverefinement of the quantization of channel state;

FIG. 8 d is flow chart of base station operations in the reconstructionof channel state from feedback information;

FIG. 9 is a data plot of the sum capacity performance for a two antennabase transceiver station with two subscriber stations as studied inprior art;

FIG. 10 is a data plot of increasing performance for a two antenna basetransceiver station with two subscriber stations using embodiments ofthe present invention;

FIG. 11 is a data plot of the sum capacity performance for a fourantenna base transceiver station with four subscriber stations asstudied in prior art; and

FIG. 12 is a data plot of increasing performance for a four antenna basetransceiver station with four subscriber stations using embodiments ofthe present invention;

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

Embodiments of the present invention provides a novel method to improveperformance of codebook-based wireless communication systems, whichresults in higher capacity and better quality links and thus improvesthe performance of a wireless system. It is understood, however, thatthe following disclosure provides many different embodiments, orexamples, for implementing different features of the invention. Specificexamples of components, signals, messages, protocols, and arrangementsare described below to simplify the present disclosure. These are, ofcourse, merely examples and are not intended to limit the invention fromthat described in the claims. Well known elements are presented withoutdetailed description in order not to obscure the present invention inunnecessary detail. For the most part, details unnecessary to obtain acomplete understanding of the present invention have been omittedinasmuch as such details are within the skills of persons of ordinaryskill in the relevant art. Details regarding control circuitry describedherein are omitted, as such control circuits are within the skills ofpersons of ordinary skill in the relevant art.

FIG. 1 illustrates a cellular communication system 100. Cellularcommunications system 100 includes a base transceiver station (BTS) 101communicates and a plurality of subscriber units 105, which may bemobile or fixed. BTS 101 and subscriber units 105 communicate usingwireless communication. BTS 101 has a plurality of transmit antennas 115while subscriber units 105 have one or more receive antennas 110. BTS101 sends control and data to subscriber units 105 through a downlink(DL) channel 120 while subscriber units 105 send control and data to BTS101 through uplink (UL) channel 125.

Subscriber units 105 may send control information on uplink channel 125to improve the quality of the transmission on downlink channel 120. BTS101 may send control information on downlink channel 120 for the purposeof improving the quality of uplink channel 125. A cell 130 is aconventional term for the coverage area of BTS 101. It is generallyunderstood that in cellular communication system 100 there may bemultiple cells corresponding to multiple BTSs.

FIG. 2 a illustrates a prior art BTS 101. Data 200 destined for aplurality of users being served, in the form of bits, symbols, orpackets for example, may be sent to a scheduler 205, which may decidewhich users will transmit in a given time/frequency opportunity.Scheduler 205 may use any of a wide range of known schedulingdisciplines in the literature including round robin, maximum sum rate,proportional fair, minimum remaining processing time, or maximumweighted sum rate. Generally scheduling decisions are based on channelquality information feedback 245 fedback from a plurality of subscriberunits.

Data from users selected for transmission are processed by modulationand coding block 210 to convert the data to transmitted symbols.Modulation and coding block 210 may also add redundancy for the purposeof assisting with error correction and/or error detection. A modulationand coding scheme implemented in modulation and coding block is chosenbased in part on information about the channel quality informationfeedback 245.

The output of modulation and coding block 205 may be passed to atransmit beamforming block 220, which maps the output (a modulated andcoded stream for each user) onto a beamforming vector. The beamformedoutputs are coupled to antennas 115 through RF circuitry, which are notshown. The transmit beamforming vectors are input from a single userblock 225 or a multi-user block 230.

Either beamforming for a single user or multiple user beamforming may beemployed, as determined by switch 235, based on information fromscheduler 205 as well as channel quality information feedback 245. Partof each user's channel quality information feedback includes an index toa codeword in codebook 215, corresponding to quantized channelinformation. The modulation/coding and beamforming may be repeated forall scheduled users based on the output from 205.

An extract codeword block 240 produces the quantized channel stateinformation based on the index received from the channel qualityinformation feedback 245. Extract codeword block 240 may use the indexto reference the codeword from codebook 215. The output of extractcodeword block 240 is passed to switch 235 that forwards the informationto either single user block 225 or multi-user block 230. Otherinformation may also be passed to these blocks, for example asignal-to-interference-plus-noise ratio (SINR) estimate may be passed tothe multi-user block 230 to improve its performance. Single user block225 uses the output of extract codeword block 240 as the beamformingvector for the selected user. Other processing may also be applied, suchas interpolation in the case that orthogonal frequency divisionmultiplexing (OFDM) modulation is employed.

Multi-user block 230 combines the codeword from codebook 215 and otherinformation from multiple users to derive the transmit beamformingvectors employed for each user. It may use any number of algorithmswidely known in the literature including zero forcing, coordinatedbeamforming, minimum mean squared error beamforming, or latticereduction aided precoding for example. Channel quality informationfeedback 245 may, for purposes of illustration, be in the form ofquantized channel measurements, modulation, coding, and/or spatialformatting decisions, received signal strength, andsignal-to-interference-plus-noise measurements, and so forth.

FIG. 2 b illustrates a prior art subscriber unit 105. Subscriber unit105 may have one or a plurality of receive antennas 110, connectingthrough RF circuitry, not shown, to a receiver signal processing block250. Some of the key functions performed by receiver signal processingblock 250 may be channel estimation 255 and estimatesignal-to-interference-plus-noise ratio (SINR) block 260. Channelestimation block 255 uses information inserted into the transmit signalin the form of training signals, training pilots, or structure in thetransmitted signal such as cyclostationarity to estimate coefficients ofthe channel between BTS 101 and subscriber unit 105.

Channel state information is quantized in a codebook-based quantizationblock 265, which uses codebook 215 (the same codebook as codebook 215 ofFIG. 2 a) also available at BTS 101. The output of quantization block265 may be the index of a codeword in codebook 215 that best correspondsto the channel state information. For example, the vector in codebook215 that is closest to the estimated channel vector in terms of minimumsubspace distance may be chosen, or the vector from codebook 215 thatmaximizes the effective SINR may be selected. The index of the codewordis provided to generate channel quality information block 270, whichgenerates channel quality information feedback 245 from the index. Thechannel quality information feedback 245 may be used to aid schedulingand transmit beamforming, for example.

To better explain the prior art and the merits of the variousembodiments, consider the following mathematical description. Considerfirst the single user transmission mode. Assuming a narrowbandtransmission (it is obvious how to extend the present results tobroadband transmission using OFDM), the signal received at user u indiscrete-time, after matched filtering and sampling, for single usertransmission may be written as

y _(u) =H _(u) f _(u) ^(#) s _(u) +v _(u)

where y_(u) is the M_(r)×1 received signal vector (where M_(r) is thenumber of receive antennas), H_(u) is the M_(r)×M_(t) channel matrix(where M_(t) is the number of transmit antennas at BTS 101) between BTS101 and user u, f_(u) ^(#) is the M_(t)×1 transmit beamforming vectordesigned for user u, s_(u) is the symbol sent to user u, and v_(u) isthe additive noise vector at subscriber u's receiver of dimensionM_(r)×1.

In prior art, the beamforming vector f_(u) ^(#) chosen at thetransmitter comes from a finite set of possible beamforming vectorsF={f₁, f₂, . . . , f_(N)}, the coefficients of which may be from anynumber of codebooks known in the literature including Grassmanniancodebooks, DFT codebooks, vector quantization codebooks, etc.

The size of the codebook is given by N and is sometimes given in bitslog₂ N. Prior art considers codebooks of size around 6 bits. Thereceiver selects the index of the best vector from the codebook at thereceiver according to any number of codeword selection criteria. Forexample, quantization block 265 may compute the optimum index as

$k_{u} = {\max\limits_{{n = 1},2,\mspace{11mu} \ldots \mspace{11mu},N}{{H_{u}f_{n}}}}$

and this index is incorporated into channel quality information feedback245 by generate channel quality information message block 270. Inanother embodiment, quantization block 265 computes the dominant rightsingular vector of H_(u) as v then computes the optimum index as

$k_{u} = {\min\limits_{{n = 1},2,\mspace{11mu} \ldots \mspace{11mu},N}{d\left( {v,f_{n}} \right)}}$

using a subspace distance like the chordal distance. BTS 101 thenextracts codeword block sets f_(u) ^(#)=f_(k*), basically the indexreceived on the feedback channel is used to generate the beamformingvector used for transmission.

Now consider one embodiment of the multiple user transmission mode. Forillustrative purposes suppose that M_(t)=2, M_(r)=1, and there are twousers a and b chosen by the scheduler. Suppose the transmit beamformingvectors are computed using the zero-forcing precoding methodology(described in T. Yoo, N. Jindal, and A. Goldsmith, Multi-AntennaDownlink Channels with Limited Feedback and User Selection, IEEE JournalSel. Areas in Communications, Vol. 25, No. 7, pp. 1478-1491, September2007 for example). The received signal at user a after matched filteringand sampling may be written as

y _(a) =H _(a) f _(a) ^(#) s _(a) +H _(a) f _(b) ^(#) s _(b) +v _(a)

where y_(a) is the M_(r)×1 received signal vector (where M_(r) is thenumber of receive antennas), H_(a) is the M_(r)×M_(t) channel matrix(where M_(t) is the number of transmit antennas at the BTS) between BTS101 and user a, f_(a) ^(#) is the M_(t)×1 transmit beamforming vectordesigned for user a, f_(b) ^(#) is the M_(t)×1 transmit beamformingvector designed for user b, s_(a) is the symbol sent to user a, s_(b) isthe symbol sent to user b, and v_(a) is the additive noise vector atsubscriber a's receiver of dimension M_(r)×1.

A similar equation may be written for user b and this equation maynaturally be generalized to more than two users. In the case of M_(r)=1the user, may employ the same quantization method as described in theprevious case to find an index for the quantized channel state inquantization block 265. Unlike the single user case, however, the usermay also send additional information like an estimate of thesignal-to-interference-plus-noise (SINR) ratio that includes effects ofquantization. The reason is that because quantized channel stateinformation is used, and there is residual interference that should beaccounted for. This may be estimated in generate channel qualityinformation block 270 using any number of techniques known in theliterature.

BTS 101 uses the SINR information in scheduler 205 to select the usersfor transmission and also to estimate their transmission rates formodulation and coding block 210. With zero forcing preceding, multi-userblock 230 may compute the transmit beamforming vector by inverting thematrix [f_(a),f_(b)], and normalizing the columns to produce thebeamforming vectors [f_(a) ^(#),f_(b) ^(#)]. Because of the effects ofresidual interference, multiuser systems as is well known in the priorart (see for example Yoo. Et. al.) require large codebook sizes, i.e., Nmay be large (for example, on the order of 4,096 or more). A majorchallenge is that it is very difficult to perform the quantization inquanitization block 265 and generate the reconstruction in extractcodeword block 240 when the codebook size is large. The problem isovercome in the embodiments.

FIG. 3 a illustrates a BTS 301. Data 200 destined for a plurality ofusers being served, in the form of bits, symbols, or packets forexample, are sent to a scheduler 205, which decides which users willtransmit in a given time/frequency opportunity. Data from users selectedfor transmission are processed by modulation and coding block 210 toconvert to transmitted symbols and add redundancy for the purpose ofassisting with error correction or error detection. The modulation andcoding scheme is chosen based in part on information about the channelquality information feedback 315.

The output of modulation and coding block 205 is passed to a transmitbeamforming block 220, which maps the modulated and coded stream foreach user onto a beamforming vector. The beamformed outputs are coupledto antennas 115 through RF circuitry. The transmit beamforming vectorsare input from single user block 225 or multi-user block 230. Eitherbeamforming for a single user or multi-user beamforming may be employed,as determined by switch 235, based on information from scheduler 205 andchannel quality information feedback 315. Part of each users channelquality information feedback includes a new progressive feedback messagethat provides indices corresponding to progressively quantized channelinformation as described in the embodiments.

Progressive reconstruction block 302 uses the indices in the channelquality information feedback 315 combined with a base codebook 305 and alocalized codebook 310 to reconstruct a high-resolution estimate of thequantized channel state information. The output of progressivereconstruction block 302 is passed to switch 235 that forwards theinformation to either the single user block 225 or the multi-user block230. Other information may also be passed to these blocks, for example aSINR estimate may be passed to the multi-user block 230 to improve itsperformance. Single user block 225 uses the output of progressivereconstruction block 302 as the beamforming vector for the selecteduser.

Multi-user block 230 combines the codeword and other information frommultiple users to derive the transmit beamforming vectors employed foreach user. It may use any number of algorithms known in the literatureincluding zero forcing, coordinated beamforming, minimum mean squarederror beamforming, or lattice reduction aided preceding, for example.

Scheduler 205 may use any of the known scheduling disciplines in theliterature including round robin, maximum sum rate, proportional fair,minimum remaining processing time, or maximum weighted sum rate;generally scheduling decisions are based on channel quality informationfeedback 315 received from the plurality of subscribers. Scheduler 205may decide to send information to a single user via transmit beamformingor may decide to serve multiple users simultaneously through multiuserMIMO communication.

Modulation and coding block 210 may perform any number of coding andmodulation techniques including quadrature amplitude modulation, phaseshift keying, frequency shift keying, differential phase modulation,convolutional coding, turbo coding, bit interleaved convolutionalcoding, low density parity check coding, fountain coding; or blockcoding. The choice of modulation and coding rate in a preferredembodiment is made based on channel quality information feedback 315 ina preferred embodiment and may be determined jointly in the scheduler205.

While not explicitly illustrated, it is obvious to those skilled in theart that OFDM modulation can be used. Further, any number of multipleaccess techniques could be used including orthogonal frequency divisionmultiple access; code division multiple access; frequency divisionmultiple access; or time division multiple access. The multiple accesstechnique may be combined with the modulation and coding block 205 orthe transmit beamforming block 220 among others.

Channel quality information feedback 315 may, for purposes ofillustration, be in the form of quantized channel measurements,modulation, coding, and/or spatial formatting decisions, received signalstrength, and signal-to-interference-plus-noise measurements.

FIG. 3 b illustrates subscriber unit 302. Subscriber unit 302 may haveone or more receive antennas 110, connecting through RF circuitry to areceiver signal processing block 250. Some of the key functionsperformed by receiver signal processing block 250 include channelestimation block 255, estimate SINR block 260, and a mobility estimateblock 325.

Channel state information is quantized using a progressive quantizationblock 330 as described in the embodiments. Progressive quantizationblock 330 first quantizes the received signal to a base codebook 305then generates at least one successive refinement using a localizedcodebook 310. With each progressive refinement, localized codebook 310becomes more localized resulting in a more efficient quantization. Anindex from the base codebook and several indices from the localizedcodebook are output form progressive quantization block 330. An estimateof the amount of channel variation, produced by mobility estimate block325, may be used to improve the progressive quantization algorithm byinitializing the algorithm from a previous quantization level oradjusting the amount of localization.

Progressive feedback block 335 generates a new feedback message bycombining the base and localized codebook indices output fromprogressive quantization block 330. Generate channel quality informationblock 340 generates a special feedback control message employing theoutputs of progressive feedback block 335 to produce channel qualityinformation feedback 315.

Channel estimation block 255 may employ any number algorithms known inthe art including least squares, maximum likelihood, maximum a postiori,Bayes estimator, adaptive estimator, or a blind estimator. Somealgorithms exploit known information inserted into the transmit signalin the form of training signals, training pilots, while others usestructure in the transmitted signal such as cyclostationarity toestimate coefficients of the channel between the BTS and the subscriber.

Estimate SINR block 260 outputs some measure of performancecorresponding to the desired signal. In one embodiment this consists ofa received signal power to interference plus noise estimate. In anotherembodiment, it provides an estimate of the received signal-to-noiseratio. In yet another embodiment, it provides an estimate of the averagereceived signal power, averaged over subcarriers in an OFDM system.

The embodiments employ a new progressive quantization algorithm toenable efficient high resolution quantization. It employs two codebooks:a base codebook 305 and a localized codebook 310. FIG. 4 a illustrates arepresentative example of base codebook 305 and FIG. 4 b illustrates arepresentative example of localized codebook 310. The codebooks areillustrated in as points, such as points 405, on a unit sphere 400.

Base codebook 305 is used in the first step in the quantization process.As such, it should be as uniform as possible. Any design known to thoseskilled in the art could be use including Grassmannian codebooks,Kerdock codebooks, mutually unbiased bases, vector quantization derivedcodebooks, etc. Different codebooks may be employed for differentnumbers of antennas. The size the codebook can also be varied. Apreferred embodiment for base codebook 305 for two transmit antennas is

$F_{{3\; {GPP}},2} = {\left\{ {\begin{bmatrix}1 \\0\end{bmatrix},\begin{bmatrix}0 \\1\end{bmatrix},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}} \right\}.}$

This codebook forms a mutually unbiased basis or Kerdock code (see T.Inoue and R. W. Heath Jr., “Kerdock codes for limited feedback MIMOsystems,” Mar. 30-Apr. 4, 2008, Proc. of the IEEE Int. Conf. onAcoustics, Speech, and Signal Proc., Las Vegas, Nev., for example) andhas also been employed for use in prior work without progressivequantization (see Samsung, “Codebook design for 4tx SU MIMO,” 3GPP TSGRAN WG1 49, Kobe, Japan, 7-11 May, 2007). It has the property that eachpair of vectors forms an orthogonal matrix and vectors from each basespair have inner product 1/√{square root over (2)}.

A preferred embodiment for base codebook 305 for three transmit antennasis

$F_{{Kerdock},3} = {\frac{1}{\sqrt{3}}{\begin{Bmatrix}{\begin{bmatrix}1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\^{{j2\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\^{{j2\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\1\end{bmatrix},} \\{\begin{bmatrix}1 \\1 \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\^{{j2\pi}/3}\end{bmatrix},{{\begin{bmatrix}3 \\0 \\0\end{bmatrix}\begin{bmatrix}0 \\3 \\0\end{bmatrix}}\begin{bmatrix}0 \\0 \\3\end{bmatrix}}}\end{Bmatrix}.}}$

Note that this codebook, except for the identity, consists ofpermutations of a 3×3 DFT matrix, thus inner products can be computedefficiently using a Fourier algorithm.

A preferred embodiment for base codebook 305 for four transmit antennasis

$F_{{3\; {GPP}},4} = {\frac{1}{2}{\begin{Bmatrix}\begin{matrix}{\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix},\begin{bmatrix}1 \\j \\1 \\{- j}\end{bmatrix},\begin{bmatrix}1 \\{\left( {{- 1} - j} \right)/\sqrt{2}} \\{- j} \\{\left( {1 - j} \right)/\sqrt{2}}\end{bmatrix},} \\{\begin{bmatrix}1 \\{\left( {1 - j} \right)/\sqrt{2}} \\j \\{\left( {{- 1} + j} \right)/\sqrt{2}}\end{bmatrix},{\quad{\begin{bmatrix}1 \\{\left( {1 + j} \right)/\sqrt{2}} \\{- j} \\{\left( {{- 1} + j} \right)/\sqrt{2}}\end{bmatrix},\begin{bmatrix}1 \\{\left( {{- 1} + j} \right)/\sqrt{2}} \\j \\{\left( {1 + j} \right)/\sqrt{2}}\end{bmatrix},}}}\end{matrix} \\{\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\{- j} \\{- 1} \\{- j}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\j \\{- 1} \\j\end{bmatrix},{\quad{\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}}}}\end{Bmatrix}.}}$

An alternative embodiment base codebook 305 that has slightly bettertheoretical properties for four transmit antennas is based on themutually unbiased bases or Kerdock code is

${F_{{Kerdock},4} = {\frac{1}{2}\begin{Bmatrix}\begin{matrix}{\begin{bmatrix}2 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\2 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\2 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\2\end{bmatrix},\begin{bmatrix}{- j} \\1 \\{- j} \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- j} \\1 \\j \\1\end{bmatrix},} \\{\begin{bmatrix}{- j} \\{- 1} \\j \\{- 1}\end{bmatrix},{\quad{\begin{bmatrix}{- 1} \\{- j} \\{- j} \\1\end{bmatrix},{\quad{\begin{bmatrix}{- 1} \\{- j} \\j \\{- 1}\end{bmatrix},{\quad{\begin{bmatrix}{- j} \\{- 1} \\{- 1} \\j\end{bmatrix},\begin{bmatrix}j \\1 \\{- 1} \\j\end{bmatrix},\begin{bmatrix}{- 1} \\{- 1} \\j \\{- j}\end{bmatrix},}}}}}}}\end{matrix} \\{\quad{\begin{bmatrix}j \\j \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\{- j} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- j} \\{- j}\end{bmatrix},\begin{bmatrix}j \\j \\j \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\{- 1}\end{bmatrix},{\quad\begin{bmatrix}{- 1} \\1 \\1 \\{- 1}\end{bmatrix}}}}\end{Bmatrix}}},$

Localized codebook 310, as shown FIG. 4 b, is one that is not uniform.More specifically it is a codebook of N_(l) vectors with the same normS={e₁, w₀, . . . , w_(N) _(l) ⁻²} that satisfy the following property.The root of the codebook is the N_(t)×1 vector

$e_{1} = {\left\lfloor \begin{matrix}1 \\0 \\\vdots \\0\end{matrix} \right\rfloor.}$

The embodiment of the root vector is chosen in this way to facilitate acomputationally simple implementation but it will be clear to thoseskilled in that art that any root vector may be chosen. Defining thesubspace distance between unit norm vectors a and b as d(a,b)=√{squareroot over (1−|a*b|²)}, a localized codebook satisfies the property thatd(e₁,w_(n))≦K for some positive constant K and d(e₁,w_(n))>0 for n=0, .. . N_(l)−2. In an embodiment of the localized codebook, the root of thecodebook is the centroid of the remaining vectors meaning that

${\begin{matrix}\min \\{,{{} = 1}}\end{matrix}{\sum\limits_{n = 0}^{N_{l} - 2}{d^{2}\left( {,w_{n}} \right)}}} > 0$

is e₁. In this way the root vector is the centroid of the localizedcodebook (shown in FIG. 4 b as point 410).

A preferred embodiment for local codebook 310 is a ring codebook, whichis conceptually illustrated in FIG. 4 b. The ring codebook has theadditional property that d(e₁,w_(n))=γ₀ for n=0, . . . N_(l)−2. Thismeans that all the non-root vectors are equidistant from the rootvector.

For two transmit antennas a preferred embodiment of the ring codebookhas vectors of the form

$w_{} = \begin{bmatrix}\sqrt{1 - \gamma_{0}^{2}} \\{\gamma_{0}^{j\; \theta_{}}}\end{bmatrix}$

with a set of uniform phases

$\theta_{} = \frac{2\; \pi \; }{N_{l} - 1}$

for l=0, 1, . . . , N_(l)−2. This choice of phases maximizes the minimumdistance between vectors in {w_(n)}_(n=0) ^(N) ^(l) ⁻² which is a goodproperty of a ring codebook.

A specific codebook that is especially easy to store and scale asγ₀=1/√{square root over (2)}. Then with N_(l)=4 a preferred embodimentfor the ring codebook is

$S_{2} = {\left\{ {\begin{bmatrix}1 \\0\end{bmatrix},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}} \right\}.}$

Another preferred embodiment for the ring codebook builds a ring using asmaller uniform base codebook. In this case the vectors of the ring havethe form

$w_{} = \begin{bmatrix}\sqrt{1 - \gamma_{0}^{2}} \\{{\overset{\sim}{w}}_{}\gamma_{0}^{j\; \theta_{}}}\end{bmatrix}$

with a set of uniform phases

$\theta_{} = \frac{2\; \pi \; }{N_{l} - 1}$

for l=0, 1, . . . , N_(l)−2, where the collection of vectors is chosenfrom any good set of base vectors for example Grassmannian codebooks.This permits some storage savings since a base codebook for two antennascan be used to build a localized ring codebook for three antennas.

A preferred embodiment for three transmit antennas is the ring codebook

$S_{3} = {\frac{1}{\sqrt{3}}{\begin{Bmatrix}{\begin{bmatrix}3 \\0 \\0\end{bmatrix},\begin{bmatrix}1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\^{j\; 2\; {\pi/3}} \\^{j\; 4\; {\pi/3}}\end{bmatrix},\begin{bmatrix}1 \\^{j\; 4\; {\pi/3}} \\^{j\; 2\; {\pi/3}}\end{bmatrix},\begin{bmatrix}1 \\^{j\; 2\; {\pi/3}} \\^{j\; 2\; {\pi/3}}\end{bmatrix},} \\{\begin{bmatrix}1 \\^{j\; 4\; {\pi/3}} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\^{j\; 4\; {\pi/3}}\end{bmatrix},\begin{bmatrix}1 \\^{j\; 2\; {\pi/3}} \\^{j\; 2\; {\pi/3}}\end{bmatrix},{\quad{\begin{bmatrix}1 \\^{j\; 2\; {\pi/3}} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\^{j\; 2\; {\pi/3}}\end{bmatrix}}}}\end{Bmatrix}.}}$

This codebook has

$\gamma_{0} = \sqrt{\frac{2}{3}}$

and has nice distance properties. In particular

${d\left( {e_{1},w_{n}} \right)} = \sqrt{\frac{2}{3}}$

for n=0, . . . , 9 and for k,n=0, . . . , 9, k≠n

${d\left( {w_{k},w_{n}} \right)} = \left\{ {\begin{matrix}{\sqrt{\frac{2}{3}}\mspace{14mu} {or}} \\1\end{matrix}.} \right.$

This means that the vectors in the ring also have good distanceproperties.

For four transmit antennas, a preferred embodiment of the ring codebookwith

$\gamma_{0} = \frac{\sqrt{3}}{2}$

is

$S_{4} = {\frac{1}{2}{\begin{Bmatrix}{\begin{bmatrix}2 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}{- j} \\1 \\{- j} \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- j} \\1 \\j \\1\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\j \\{- 1}\end{bmatrix},\begin{bmatrix}{- 1} \\{- j} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- 1} \\{- j} \\j \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- 1} \\j\end{bmatrix},\begin{bmatrix}j \\1 \\{- 1} \\j\end{bmatrix},} \\{\quad{\begin{bmatrix}{- 1} \\{- 1} \\j \\{- j}\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\{- j} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- j} \\{- j}\end{bmatrix},\begin{bmatrix}j \\j \\j \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}{- 1} \\1 \\1 \\{- 1}\end{bmatrix}}}\end{Bmatrix}.}}$

In particular note that

${d\left( {e_{1},w_{n}} \right)} = \sqrt{\frac{2}{3}}$

for n=0, . . . , 15 and for k,n=0, . . . , 15, k≠n

${d\left( {w_{k},w_{n}} \right)} = \left\{ \begin{matrix}{\frac{\sqrt{3}}{2}\mspace{14mu} {or}} \\1.\end{matrix} \right.$

The embodiments of ring codebooks S₂, S₃, and S₄ all contain a subset ofvectors in the mutually unbiased bases or Kerdock code. Thus otherpreferred embodiments can be constructed for larger numbers of transmitantennas from the corresponding mutually unbiased bases, as is apparentto those skilled in the art. Also, it should be apparent that if themutually unbiased bases were chosen for the base codebook that a subsetof the vectors could be used for the localized codebook. Thus thelocalized codebook could be a subset of the base codebook, offeringsavings in terms of storage and memory.

Though localized ring codebooks are preferred, other localized codebooksmay also be employed by embodiments. FIG. 5 a illustrates a localizedconcentric ring codebook. The localized concentric ring codebook hasmultiple concentric rings 500 of vector codewords in addition tocentroid 410. Rings 500 have different radii. FIG. 5 b illustratesanother localized codebook. The localized codebook shown in FIG. 5 b hasseveral rotated rings 510 of vector codewords in addition to thecentroid 410. Rings 510 are rotated to have a larger maximum minimumdistance and improve performance, for example. FIG. 5 c illustrates yetanother localized codebook. The localized codebook shown in FIG. 5 c hasvectors 515 that all belong inside a disc 520. This has the advantage ofpotentially having a larger maximum minimum distance between codevectors.

FIGS. 6 a through 6 c illustrates the operation of progressivequantization block 330, which exploits the special structure given bythe base codebook and the localized codebook. The diagrams shown inFIGS. 6 a through 6 c are intended to provide a conceptual illustrationof the embodiments. As shown in FIG. 6 a, an observation 600 may bequantized into a quantization value using base codebook 305. Then, asshown in FIG. 6 b, a localized ring codebook is rotated so that the rootvector aligns with the quantized value 605 and the quantization with thelocalized ring codebook is performed over the vectors in the rotatedring, resulting in a new quantized value 610. This is the output of thefirst refinement.

In the next refinement, as shown in FIG. 6 c, the localized ringcodebook is scaled so that the radius is smaller and the quantizationprocess repeats, producing another new quantized value 620. Therefinement process may be repeated for an arbitrary number ofrefinements to produce quantized values that converge towardsobservation 600.

The output of progressive quantization block 330 consists of an index inthe base codebook and several refinement indices that correspond to thelocalized codebook, with the number of refinement indices beingdependent on the number of times the refinement was performed.

FIG. 7 a illustrates the generation of feedback message bits from thecodebook indices. Progressive feedback block 335 can combine thecodebook indices in several different ways to produce a feedbackmessage. In one embodiment, a base index 700 and refinement index one705 and refinement index two 710 are concatenated together to form asingle feedback message 715. Additional error protection 720 may beemployed to provide resilience to errors in the feedback channel.

FIG. 7 b illustrates the generation of feedback message bits from thecodebook indices. In another embodiment, base index 700, refinementindex 705, and refinement index two 710 are combined together in acombine block 725 to produce a potentially shorter feedback message 715.The advantage of this embodiment is that it reduces the amount offeedback required when the size of the localized codebook is not a powerof two. It will be clear to those skilled in the art that multiplerefinements may similarly be included in the feedback message in eitherpreferred embodiment. Again, error protection 720 may be employed toprovide resilience to errors in the feedback channel.

The application of the error protection to the feedback message 715 mayprovide a different level of error protection for different codebookindices. For example, the base index may be given the highest level oferror protection, while the refinement indices may be given a lowerlevel of error protection. Alternatively, the level of error protectionmay progressively decrease for each level of refinement. In yet anotheralternative, error protection may be given to a specified number ofrefinement indices (in addition to the base index) and any additionalrefinement indices may be transmitted without error protection.

A preferred embodiment of progressive quantization block 330 useslocalized codebook scaling and rotation operations. Let U(v) be thefunction that determines a unitary matrix that rotates vector v to theroot vector e₁ thus e₁=U(v)v. In a preferred embodiment such a rotationmatrix is computed from the singular value decomposition of v; inanother embodiment it is computed using successive Given's rotations. Itwill be necessary to rotate the codebook to align it with a vector v.Define the rotated version of localized codebook S as

r(S,v)={U(v)e ₁ ,U(v)w ₀ ,U(v)w ₁ , . . . , U(v)w _(N) _(l) ⁻²}.

It will also be necessary to scale diameter of the localized codebookfrom radius γ₀ by γ to produce a localized codebook γγ₀. Define thevector scaling operation as follows: Write the coefficients of a vectorw using polar form as

$w = {\begin{bmatrix}{r_{1}^{{j\; \theta_{1}}\;}} \\{r_{2}^{j\; \theta_{2}}} \\\vdots \\{r_{N_{t}}^{j\; \theta_{N_{t}}}}\end{bmatrix}.}$

Now define the scaling function of w as

${s\left( {w,\alpha} \right)} = {\begin{bmatrix}{\sqrt{1 - {\alpha^{2}\left( {1 - r_{1}^{2}} \right)}}^{j\; \theta_{1}}} \\{\alpha \; r_{2}^{j\; \theta_{2}}} \\\vdots \\{\alpha \; r_{M_{t}}^{j\; \theta_{M_{t}}}}\end{bmatrix}.}$

Now define the localized codebook scaling function ass(S,γ)=S(γ)={s(e₁,γ),s(w₀,γ),s(w₁,γ), . . . , s(w_(N) _(l) ⁻²,γ)}. Notethat the scaling operation is such that s(e₁,γ)=e₁ and thatd(e₁,s(w_(n),γ))=γγ₀ for w_(n) that are in a localized ring codebook ofradius γ₀.

FIG. 8 a illustrates a flow diagram of operations 802 in progressivequantization block 330. Operations 802 may begin with the estimating ofthe channel to produce a channel estimate (block 805). The estimating ofthe channel may be performed by estimate channel block 255. Afterestimating the channel, the channel estimate may be normalized andquantized using the base codebook (block 807).

Let h denote the vector of channel coefficients that have beennormalized to have ∥h∥=1. Then in one preferred embodiment the initialbase quantization is performed by solving

$f_{0}^{\#} = {\begin{matrix}\min \\{f \in F}\end{matrix}{d\left( {h,f} \right)}}$

where F is the base codebook. The index of the base codebook is producedby solving

$k_{0} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{14mu},{N - 1}}\end{matrix}{{d\left( {h,f_{n}} \right)}.}}$

After performing the base quantization, operations 802 may perform anumber, such as R refinements. In general, for an r^(th) refinementstage, operations 802 includes scaling the localized codebook to producescaled codebook S_(s)=s(S,γ^(2r)) (block 809). Then the scaled codebookis rotated to align with the previously quantized value (block 811).

For example, in the first refinement the scaled codebook is rotated toproduce S_(r)=r(S_(s),f₀ ^(#)). Then the scaled and rotated localizedcodebook is used to produce the next best refinement solving

$f_{1}^{\#} = {\begin{matrix}\min \\{f \in S_{r}}\end{matrix}{d\left( {h,f} \right)}}$

and index of the first refinement is produced by solving

$\begin{matrix}{k_{1} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{14mu},{N_{l} - 2},{f_{n} \in S_{r}}}\end{matrix}{d\left( {h,f_{n}} \right)}}} & \;\end{matrix}$

(block 813). The r^(th) refinement f_(r) ^(#) is computed using f_(r−1)^(#) from the previous stage and the output is f_(r) ^(#) and k_(r).Operations 802 may loop until all R refinements are complete (block815).

FIG. 8 b illustrates a flow diagram of operations 817 in progressivequantization block 330. Operations 817 may begin with the estimating ofthe channel to produce a channel estimate (block 820). The estimating ofthe channel may be performed by estimate channel block 255. Afterestimating the channel, the channel estimate may be normalized andquantized using the base codebook (block 822).

Let h denote the vector of channel coefficients that have beennormalized to have ∥h∥=1. Then in one preferred embodiment the initialbase quantization is performed by solving

$f_{0}^{\#} = {\begin{matrix}\min \\{f \in F}\end{matrix}{d\left( {h,f} \right)}}$

where F is the base codebook. The index of the base codebook is producedby solving

$k_{0} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{14mu},{N - 1}}\end{matrix}{{d\left( {h,f_{n}} \right)}.}}$

After performing the base quantization, operations 817 may perform anumber, such as R, of refinements. In general, for an r^(th) refinementstage, operations 817 includes scaling the localized codebook to producescaled codebook S_(s)=s(S,γ^(2r)) (block 824). Then, instead of rotatingthe scaled localized codebook, the observed vector is rotated asU*(f_(r−1) ^(#))h, where U*(f_(r−1) ^(#)) is the conjugate transpose ofU(f_(r−1) ^(#)) (block 826). Then the scaled localized codebook is usedto produce the next best refinement solving

$f_{r}^{\#} = {\begin{matrix}\min \\{f \in S_{r}}\end{matrix}{d\left( {{{U^{*}\left( f_{r - 1}^{\#} \right)}h},f} \right)}}$

and index of the first refinement is produced by solving

$k_{r} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{14mu},{N_{l} - 2},{f_{n} \in S_{r}}}\end{matrix}{d\left( {{{U^{*}\left( f_{r - 1}^{\#} \right)}h},f_{n}} \right)}}$

(block 828). This approach has an implementation advantage in thatcomputations to rotate the scaled codebook are not required. Operations817 may loop until all R refinements are complete (block 830).

FIG. 8 c illustrates a flow diagram of operations 832 in progressivequantization block 330. Operations 832 may begin with the estimating ofthe channel to produce a channel estimate (block 835). The estimating ofthe channel may be performed by estimate channel block 255. Afterestimating the channel, the channel estimate may be normalized andquantized using the base codebook (block 837).

Let h denote the vector of channel coefficients that have beennormalized to have ∥h∥=1. Then in one preferred embodiment the initialbase quantization is performed by solving

$f_{0}^{\#} = {\begin{matrix}\min \\{f \in F}\end{matrix}{d\left( {h,f} \right)}}$

where F is the base codebook. The index of the base codebook is producedby solving

$k_{0} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{14mu},{N - 1}}\end{matrix}{{d\left( {h,f_{n}} \right)}.}}$

After performing the base quantization, operations 832 may perform anumber, such as R refinements. In general, for an r^(th) refinementstage, operations 832 includes scaling the observation vector (block839). Define a scaled version of vector w as

${t\left( {w,\alpha} \right)} = \begin{bmatrix}{\sqrt{1 - {\alpha^{2}\left( {1 - {1/}} \right)}}w^{(1)}} \\{\alpha \; \overset{\sim}{w}}\end{bmatrix}$

where

$w = \begin{bmatrix}w^{(1)} \\\overset{\sim}{w}\end{bmatrix}$

and w⁽¹⁾ is the first entry of w. Then, form the scaled input vectorh_(s)=t(h,γ^(2r)). Then, form the rotated vector U*(f_(r−1) ^(#))h_(s)(block 841). Finally, the localized codebook is used to produce the nextbest refinement solving

$f_{r}^{\#} = {\begin{matrix}\min \\{f \in S}\end{matrix}{d\left( {{{U^{*}\left( f_{r - 1}^{\#} \right)}h_{s}},f} \right)}}$

and index of the first refinement is produced by solving

$k_{r} = {\begin{matrix}\min \\{{n = 0},\ldots \mspace{11mu},{N_{l} - 2},{f_{n} \in S}}\end{matrix}{d\left( {{{U^{*}\left( f_{r - 1}^{\#} \right)}h_{s}},f_{n}} \right)}}$

(block 843). This approach has an implementation advantage in thatscaling of the codebook is also not required thus further lowering thecomplexity. Operations 832 may loop until all R refinements are complete(block 845).

FIG. 8 d illustrates a flow diagram of operations 847 in progressivereconstruction block 300. Operations 847 may begin receiving channelquality information feedback (or feedback bits) from a receiver (block850). From the channel quality information feedback, a base index andrefinement index(s) may be extracted (block 852). The base andrefinement indices may be denoted k₀, k₁, . . . , k_(R). Let f_(k) ₀denote the vector chosen from the base codebook and let z_(k) _(r)denote the vector chosen from the scaled localized codebook s(S,γ^(2r)).Then the reconstructed estimate of the quantized normalized vector h iscomputed as ĥ=U( . . . U(U(f_(k) ₀ )z_(k) ₁ )z_(k) ₂ . . . )z_(k) _(R) )(block 854).

Then, operations 847 may perform a number, such as R, of refinements. Ingeneral, for an r^(th) refinement stage, operations 847 includes usingthe previous refinement, denoted by ĥ_(r−1), to produceĥ_(r)=U(ĥ_(r−1))z_(k) _(r) , which includes scaling the localizedcodebook by the r^(th) refinement index and applying the r^(th)refinement to the reconstructed estimate (blocks 856 and 858). The finaloutput is ĥ=ĥ_(R) produced after all R refinements have been performed(blocks 860 and 862).

It will be obvious to those of ordinary skill in the art that this isjust one example of a way to reconstruct the quantized vector. Forexample, the scaled localized codebooks used in block 839 could beprecomputed. Several different techniques can be used to solve for therotation vector including the singular value decomposition and Givensrotations.

The scaling factor γ is a parameter of the progressive refinementalgorithm. To perform reconstruction it should be known at thetransmitter and the receiver. In a preferred embodiment γ=γ₀.

The base codebook 305 and localized codebook 310 must be known both atthe BTS and at each subscriber unit. These codebooks could bepre-designed or they could be dynamically downloaded in the system. Theycan also be precomputed and stored in memory, or they may be computeddynamically according to some mathematical algorithm, as known to thoseof ordinary skill in the art. In a preferred embodiment, the localizedcodebook is derived by taking a subset of vectors from the basecodebook. This reduces storage requirements even further.

The number of refinements R used in the progressive refinement algorithmdetermines the amount of feedback required in the system. The larger thevalue of R, the larger the amount of feedback required. In multi-usercommunication systems, different users could be assigned differentvalues of R. For example, users with more mobile channels as determinedby mobility estimate 325 may be assigned a smaller R while users with aless mobile channel may be assigned a larger value of R.

The mobility estimate generated from mobility estimate block 325 may beused to adjust the operation of the progressive quantization algorithm.In one preferred embodiment, the progressive quantization algorithmexploits slowly varying channels in time. It may do this by not startingthe quantization using the base codebook, but by using the localizedcodebook at radius γ^(2m) where the value of m is chosen based on themobility estimate block 325. A larger value of m means the channel ismore stationary thus a smaller region can be searched while a smallervalue of m means that the channel is changing more quickly and thus alarger region must be explored. Using the progressive refinementalgorithm as described, the subscriber can reduce the amount of feedbackrequired. In a preferred embodiment only the value of m and the indicesof the refinements from m, m+1, . . . R need to be fed back. This canreduce overall feedback requirements.

FIG. 9 illustrates performance in terms of estimated sum rate for acommunication system with two transmit antennas at the base station andtwo subscriber units, assuming Rayleigh fading channels and zero-forcingtransmit beamforming as used in N. Jindal, MIMO Broadcast Channels withFinite Rate Feedback, IEEE Trans. Information Theory, Vol. 52, No. 11,pp. 5045-5059, November 2006. Quantization using either the Kerdock code(displayed as a first trace 905) or the 3GPP code (displayed as a secondtrace 910) gives poor performance relative to the unquantized zeroforcing solution (displayed as a third trace 915). FIG. 10 illustratesthe improved performance obtained using the successive refinementalgorithm. Additional refinements close the gap between quantizationusing the base codebook and the zero-forcing case with perfect channelstate information (displayed as trace 1005).

FIG. 11 illustrates performance in terms of estimated sum rate for acommunication system with four transmit antennas at the base station andfour subscriber units, assuming Rayleigh fading channels andzero-forcing transmit beamforming as used in N. Jindal, MIMO BroadcastChannels with Finite Rate Feedback, IEEE Trans. Information Theory, Vol.52, No. 11, pp. 5045-5059, November 2006. Quantization using either theKerdock code or the 3GPP code (displayed collectively as a first trace1105) gives poor performance relative to the unquantized zero forcingsolution (displayed as a second trace 1110). FIG. 12 illustrates theimproved performance obtained using the successive refinement algorithm.Additional refinements close the gap between quantization using the basecodebook and the zero-forcing case with perfect channel stateinformation (displayed as trace 1205) as with the two antenna case.

Embodiments may be used in a variety of contexts. MIMO communication,where multiple antennas are used at the transmitter and receiver, is arelatively new technology. While it is deployed in wireless local areanetworks (WLANs), it is not as extensively deployed in cellular systems.It will likely be employed in the next release of HSDPA as well as inWiMax, 3PP LTE, and later IEEE 802.16m. Limited feedback has beendiscussed in several standards but has not yet been extensivelydeployed. One reason is probably the general skepticism associated withMIMO communication. Another reason is that limited feedback requires anaccurate and low delay feedback link, which cannot always be guaranteed.3GPP LTE, which has a codebook-based limited feedback mode, proposes tosolve the limited feedback problem by choosing a vector from apredetermined codebook. The codebook is not localized nor is aprogressive algorithm applied to improve quantization. Codebooks andalgorithms for the multiuser case are not yet available.

Consequently, like adaptation has not been extensively deployed ininterference limited cellular systems and real results on adaptation arenot widely known. Existing systems perform link adaptation based on SNRand SINR measurements. It is likely that the same techniques will alsobe employed in MIMO cellular systems. Essentially only the estimatedchannel and the total interference power will be used to estimate theoptimum transmit mode.

Summarizing a preferred embodiment, a system and method is proposed forprogressively quantizing channel state information for application in aMIMO (multiple input multiple output) communication system. In what iscommonly known as limited feedback, channel state information at thereceiver is quantized by choosing a representative element from acodebook known to both the receiver and transmitter. Unfortunately, highresolution representation of the channel state information, as requiredwith multiuser MIMO communication, is challenging due to the large sizecodebooks required.

Embodiments present a solution to this problem. Using a speciallydesigned codebook, a receiver progressively quantizes the channel stateinformation using a new method and conveys the results back to thetransmitter. The transmitter can then reconstruct the quantizedinformation with high precision. There are several key components of theproposed system including a progressive feedback control channel andprogressive refinement operation. Preferred embodiments for single userand multiuser communication systems are described.

A system for limited feedback in a MIMO communication system thatprogressively refines quantization of a channel parameter has beendescribed herein. The system includes a progressive refinement blockthat employs various algorithms. Preferred embodiments use the differentcodebooks described above. The number of refinement levels may beadjusted based on the users' channel conditions or other systemdependent parameters. When a users channel is varying slowly, instead ofsending back all the refinements, progressive refinement mightinitialize on the previous quantized value and only search over a fewrefinements. The number of refinements may depend on the operating SNR.This further reduces the feedback required. Feedback may be sent overdedicated channels or random access channels.

A system for limited feedback in a multiuser MIMO communication systemprogressively refines quantization of a channel parameter has beendescribed herein. The system includes a progressive refinement blockthat employees the algorithms described above. Preferred embodiments usethe different codebooks combined with zero-fording transmit preceding,e.g., as described in T. Yoo, N. Jindal, and A. Goldsmith,“Multi-antenna Downlink Channels with Limited Feedback and UserSelection,” IEEE J. Select. Areas Commun., vol. 25, no. 7, pp.1478-1491, September 2007. Other types of precoding may be possible. Thenumber of refinement levels may be adjusted based on the users' channelconditions or other system dependent parameters. For example, it isknown from D. J. Ryan, I. V. L. Clarkson, I. B. Collins, D. Guo, and M.L. Honig, “QAM Codebooks for Low-Complexity Limited Feedback MIMOBeamforming,” Proc. of ICC 2007, pp. 4162-4167 that for larger SNR,users require a larger codebook size while for smaller operating SNR,smaller codebooks may work. Scheduled users may be allocated morerefinements while other users may be allocated fewer refinements. Ingeneral with scheduling, less feedback per user will be required. When ausers channel is varying slowly, instead of sending back all therefinements, progressive refinement might initialize on the previousquantized value and only search over a few refinements. This furtherreduces the feedback required. Feedback may be sent over dedicatedchannels or random access channels.

A first embodiment includes a system for limited feedback in a MIMOcommunication system that progressively refines quantization of achannel parameter. This can include a 2 antenna localized codebookpreferred design or a 4 antenna localized codebook based on preferreddesign, as examples. The system can adapt the number of refinements andfeedback increments can be sent back.

A second embodiment includes a system for limited feedback in amultiuser MIMO communication system that progressively refinesquantization of a channel parameter for each user. Once again, this caninclude a 2 antenna localized codebook preferred design or a 4 antennalocalized codebook based on preferred design, as examples. The systemcan adapt the number of refinements and feedback increments can be sentback. Different numbers of refinements can be used for different usersbased on auxiliary information such as the degrees of mobility orlocation for each user. A scheduler determines the number ofrefinements.

In addition to using a separate base codebook and a separate localizedcodebook, it may be possible to use a composite codebook that combinesboth a base codebook and a localized codebook. Again, both the BTS andthe subscriber station should have its own copy of the compositecodebook. Table 1 shows an exemplary composite codebook.

TABLE 1 Composite Codebook (C(4, 1, 6, m)) BINARY INDEX M C(4, 1, 6, m)000000 0 0.5000 −0.5000   0.5000 −0.5000 000001 1 −0.5000 −0.5000  0.5000   0.5000 000010 2 −0.5000   0.5000   0.5000 −0.5000 000011 30.5000   0.0000 − 0.5000i   0.5000   0.0000 − 0.5000i 000100 4 −0.5000  0.0000 − 0.5000i   0.5000   0.0000 + 0.5000i 000101 5 −0.5000  0.0000 + 0.5000i   0.5000   0.0000 − 0.5000i 000110 6 0.5000   0.5000  0.5000   0.5000 000111 7 0.5000   0.0000 + 0.5000i   0.5000   0.0000 +0.5000i 001000 8 0.5000   0.5000   0.5000 −0.5000 001001 9 0.5000  0.0000 + 0.5000i −0.5000   0.0000 + 0.5000i 001010 10 0.5000 −0.5000  0.5000   0.5000 001011 11 0.5000   0.0000 − 0.5000i −0.5000   0.0000 −0.5000i 001100 12 0.5000   0.3536 + 0.3536i   0.0000 + 0.5000i −0.3536 +0.3536i 001101 13 0.5000 −0.3536 + 0.3536i   0.0000 − 0.5000i   0.3536 +0.3536i 001110 14 0.5000 −0.3536 − 0.3536i   0.0000 + 0.5000i   0.3536 −0.3536i 001111 15 0.5000   0.3536 − 0.3536i   0.0000 − 0.5000i −0.3536 −0.3536i 010000 16 0.5000 −0.4619 − 0.1913i   0.3536 + 0.3536i −0.1913 −0.4619i 010001 17 0.3117   0.6025 + 0.1995i −0.4030 − 0.4903i −0.1122 −0.2908i 010010 18 0.3117 −0.6025 − 0.1995i −0.1122 − 0.2908i   0.4030 +0.4903i 010011 19 0.3058   0.1901 − 0.6052i   0.1195 + 0.2866i   0.4884− 0.4111i 010100 20 0.5000 −0.1913 + 0.4619i −0.3536 − 0.3536i   0.4619− 0.1913i 010101 21 0.5000   0.1913 − 0.4619i −0.3536 − 0.3536i−0.4619 + 0.1913i 010110 22 0.5000   0.4619 + 0.1913i   0.3536 + 0.3536i  0.1913 + 0.4619i 010111 23 0.3082   0.0104 + 0.3151i   0.4077 +0.4887i −0.4783 + 0.4145i 011000 24 0.3117   0.3573 − 0.2452i   0.6025 −0.1995i −0.1578 + 0.5360i 011001 25 0.3117   0.2452 + 0.3573i −0.6025 +0.1995i   0.5360 + 0.1578i 011010 26 0.3082 −0.3666 + 0.2426i   0.6092 −0.1842i   0.1615 − 0.5298i 011011 27 0.3117 −0.2452 − 0.3573i −0.6025 +0.1995i −0.5360 − 0.1578i 011100 28 0.3117   0.4260 + 0.0793i   0.1995 +0.6025i   0.2674 + 0.4906i 011101 29 0.3117 −0.0793 + 0.4260i −0.1995 −0.6025i   0.4906 − 0.2674i 011110 30 0.3117 −0.4260 − 0.0793i   0.1995 +0.6025i −0.2674 − 0.4906i 011111 31 0.3117   0.0793 − 0.4260i −0.1995 −0.6025i −0.4906 + 0.2674i 100000 32 0.5636 −0.3332 − 0.2672i   0.1174 +0.5512i −0.3308 − 0.2702i 100001 33 0.5587   0.3361 + 0.2735i −0.3361 −0.2735i −0.1135 − 0.5471i 100010 34 0.5587 −0.3361 − 0.2735i −0.1135 −0.5471i   0.3361 + 0.2735i 100011 35 0.5587   0.2735 − 0.3361i  0.1135 + 0.5471i   0.2735 − 0.3361i 100100 36 0.3082 −0.4887 + 0.4077i−0.6092 − 0.1842i   0.2837 − 0.1205i 100101 37 0.5636   0.2673 − 0.3331i−0.1222 − 0.5501i −0.2673 + 0.3331i 100110 38 0.5636   0.3691 + 0.5142i  0.3331 + 0.2673i   0.0862 + 0.3032i 100111 39 0.5587 −0.2990 + 0.0880i  0.3361 + 0.2735i −0.5216 + 0.3616i 101000 40 0.5587   0.0880 − 0.2990i  0.3361 − 0.2735i −0.3616 + 0.5216i 101001 41 0.5587   0.2990 + 0.0881i−0.3362 + 0.2735i   0.5216 + 0.3616i 101010 42 0.5587 −0.0880 + 0.2990i  0.3361 − 0.2735i   0.3616 − 0.5216i 101011 43 0.5587 −0.2990 − 0.0880i−0.3361 + 0.2735i −0.5216 − 0.3616i 101100 44 0.5636   0.2741 − 0.1559i  0.2672 + 0.3332i   0.1081 + 0.6236i 101101 45 0.5636   0.1559 +0.2741i −0.2672 − 0.3332i   0.6236 − 0.1081i 101110 46 0.5587 −0.2737 +0.1492i   0.2735 + 0.3361i −0.1132 − 0.6245i 101111 47 0.5587 −0.1492 −0.2737i −0.2735 − 0.3361i −0.6245 + 0.1132i 110000 48 0.5000 −0.4619 +0.1913i   0.3536 − 0.3536i −0.1913 + 0.4619i 110001 49 0.3117   0.4030 +0.4903i −0.6025 − 0.1995i −0.1122 − 0.2908i 110010 50 0.3117 −0.4029 −0.4904i −0.1184 − 0.2883i   0.6067 + 0.1865i 110011 51 0.3082   0.4887 −0.4077i    .1205 + 0.2837i   0.1842 − 0.6092i 110100 52 0.5000  0.1913 + 0.4619i −0.3536 + 0.3536i −0.4619 − 0.1913i 110101 53 0.5000−0.1913 − 0.4619i −0.3536 + 0.3536i   0.4619 + 0.1913i 110110 54 0.5000  0.4619 − 0.1913i   0.3536 − 0.3536i   0.1913 − 0.4619i 110111 550.3117 −0.2452 + 0.3573i   0.6025 + 0.1995i −0.5360 + 0.1578i 111000 560.3117   0.3117 − 0.0000i   0.4030 − 0.4903i −0.4030 + 0.4903i 111001 570.3117 −0.0000 + 0.3117i −0.4030 + 0.4903i   0.4903 + 0.4030i 111010 580.3082 −0.3152 − 0.0036i   0.4076 − 0.4888i   0.4040 − 0.4872i 111011 590.3082   0.0036 − 0.3152i −0.4076 + 0.4888i −0.4872 − 0.4040i 111100 600.3117   0.2204 + 0.2204i   0.4903 + 0.4030i   0.0618 + 0.6317i 11110161 0.3117 −0.2204 + 0.2204i −0.4903 − 0.4030i   0.6317 − 0.0618i 11111062 0.3082 −0.2154 − 0.2302i   0.4887 + 0.4077i −0.0451 − 0.6313i 11111163 0.3082   0.2254 − 0.2204i −0.4888 − 0.4076i −0.6302 + 0.0588i

As shown in Table 1, codewords corresponding to indices (m) 0 through 15may be considered part of the base codebook, indices greater than 15 arecombination base codebook and localized codebook.

Using a composite codebook may have an advantage in the computation ofthe feedback message bits. For example, selecting a codeword between 0through 15 would mean that only the base codebook is used and that onlyfour feedback bits need to be fedback, while a codeword between 16 and63 is selected, then both the base codebook and the localized codebookwas used and six feedback bits are to be fedback. In an alternativeembodiment, even if a codeword between 16 and 63 is selected, it may bepossible to fedback just the two bits corresponding to the localizedcodebook portion. In this embodiment, the index to the localizedcodebook may be used in reference to a previously fedback base codebookindex.

Although the embodiments and their advantages have been described indetail, it should be understood that various changes, substitutions andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims. Moreover, thescope of the present application is not intended to be limited to theparticular embodiments of the process, machine, manufacture, compositionof matter, means, methods and steps described in the specification. Asone of ordinary skill in the art will readily appreciate from thedisclosure of the present invention, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed, that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized according to the present invention.Accordingly, the appended claims are intended to include within theirscope such processes, machines, manufacture, compositions of matter,means, methods, or steps.

1. A method for subscriber unit operation in a wireless communicationssystem, the wireless communications system having a base station, themethod comprising: computing an estimate of a communications channelbetween the subscriber unit and the base station; quantizing theestimate with a first codebook, thereby producing a first quantizedestimate; quantizing an (n−1)-th quantized estimate with an n-thcodebook, thereby producing an n-th quantized estimate, where n is aninteger value ranging from 2 to R and n initially being equal to 2, R isa total number of quantizations of the estimate, wherein the n-thcodebook is a localized codebook; incrementing n; repeating thequantizing an (n−1)-th quantized estimate until n>R; and transmittinginformation based on the R quantized estimates to the base station. 2.The method of claim 1, further comprising prior to the quantizing an(n−1)-th quantized estimate, scaling the n-th codebook.
 3. The method ofclaim 2, further comprising after the scaling the n-th codebook,rotating the n-th codebook.
 4. The method of claim 2, further comprisingafter the scaling the n-th codebook, rotating the (n−1)-th quantizedestimate.
 5. The method of claim 1, further comprising prior to thequantizing an (n−1)-th quantized estimate: scaling the (n−1)-thquantized estimate; and rotating the (n−1)-th quantized estimate.
 6. Themethod of claim 5, wherein the n-th codebook and the (n−1)-th codebookare identical.
 7. The method of claim 1, wherein the first codebook is abase codebook.
 8. The method of claim 7, wherein the first codebookcomprises a Grassmannian codebook, a Kerdock codebook, a mutuallyunbiased base codebook, or a vector quantization derived codebook. 9.The method of claim 7, wherein the base station has two transmitantennas, wherein the first codebook is expressible as:$F_{{3{GPP}},2} = {\left\{ {\begin{bmatrix}1 \\0\end{bmatrix},\begin{bmatrix}0 \\1\end{bmatrix},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}} \right\}.}$
 10. The method of claim 7, wherein the basestation has three transmit antennas, wherein the first codebook isexpressible as: $F_{{Kerdock},3} = {\frac{1}{\sqrt{3}}{\begin{Bmatrix}{\begin{bmatrix}1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\^{j\; 2{\pi/3}} \\^{j\; 4{\pi/3}}\end{bmatrix},\begin{bmatrix}1 \\^{j\; 4{\pi/3}} \\^{j\; 2{\pi/3}}\end{bmatrix},\left\lbrack \begin{matrix}1 \\{ ^{j\; 2{\pi/3}}} \\^{j\; 2{\pi/3}}\end{matrix} \right\rbrack,} \\{\begin{bmatrix}1 \\^{j\; 4{\pi/3}} \\1\end{bmatrix},\left\lbrack \begin{matrix}1 \\1 \\^{j\; 4{\pi/3}}\end{matrix} \right\rbrack,\begin{bmatrix}1 \\^{{j4\pi}/3} \\^{j\; 4{\pi/3}}\end{bmatrix},} \\{\left\lbrack \begin{matrix}1 \\^{j\; 2{\pi/3}} \\1\end{matrix} \right\rbrack ,\begin{bmatrix}1 \\1 \\^{j\; 2{\pi/3}}\end{bmatrix},{{\begin{bmatrix}3 \\0 \\0\end{bmatrix}\begin{bmatrix}0 \\3 \\0\end{bmatrix}}\begin{bmatrix}0 \\0 \\3\end{bmatrix}}}\end{Bmatrix}.}}$
 11. The method of claim 7, wherein the base stationhas four transmit antennas, wherein the first codebook is expressibleas: $F_{{3{GPP}},4} = {\frac{1}{2}{\begin{Bmatrix}{\begin{bmatrix}1 \\{- 1} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- j} \\1 \\j\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\1\end{bmatrix},\begin{bmatrix}1 \\j \\1 \\{- j}\end{bmatrix},} \\{\begin{bmatrix}1 \\{\left( {{- 1} - j} \right)/\sqrt{2}} \\{- j} \\{\left( {1 - j} \right)/\sqrt{2}}\end{bmatrix},\begin{bmatrix}1 \\{\left( {1 - j} \right)/\sqrt{2}} \\j \\{\left( {{- 1} + j} \right)/\sqrt{2}}\end{bmatrix},\begin{bmatrix}1 \\{\left( {1 + j} \right)/\sqrt{2}} \\{- j} \\{\left( {{- 1} + j} \right)/\sqrt{2}}\end{bmatrix},} \\{\begin{bmatrix}1 \\{\left( {{- 1} + j} \right)/\sqrt{2}} \\j \\{\left( {1 + j} \right)/\sqrt{2}}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\{- j} \\{- 1} \\{- j}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\{- 1}\end{bmatrix},} \\{\begin{bmatrix}1 \\j \\{- 1} \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\1 \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\1 \\1 \\1\end{bmatrix}}\end{Bmatrix}.}}$
 12. The method of claim 7, wherein the base stationhas four transmit antennas, wherein the first codebook is expressibleas: $F_{{Kerdock},4} = {\frac{1}{2}{\begin{Bmatrix}{\begin{bmatrix}2 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\2 \\0 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\2 \\0\end{bmatrix},\begin{bmatrix}0 \\0 \\0 \\2\end{bmatrix},\begin{bmatrix}{- j} \\1 \\{- j} \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- j} \\1\end{bmatrix},} \\{\begin{bmatrix}{- j} \\1 \\j \\1\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\j \\{- 1}\end{bmatrix},\begin{bmatrix}{- 1} \\{- j} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- 1} \\{- j} \\j \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- 1} \\j\end{bmatrix},\begin{bmatrix}j \\1 \\{- 1} \\j\end{bmatrix},} \\{\begin{bmatrix}{- 1} \\{- 1} \\j \\{- j}\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\{- j} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- j} \\{- j}\end{bmatrix},} \\{\begin{bmatrix}j \\j \\j \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}{- 1} \\1 \\1 \\{- 1}\end{bmatrix}}\end{Bmatrix}.}}$
 13. The method of claim 1, wherein the n-th codebookcomprises a localized codebook.
 14. The method of claim 13, wherein then-th codebook comprises a scaled version of the (n−1)-th codebook. 15.The method of claim 13, wherein the n-th codebook comprises a ringcodebook, a concentric ring codebook, a concentric-rotated ringcodebook, or a disc codebook.
 16. The method of claim 13, wherein thebase station has two transmit antennas, and wherein the n-th codebook isa ring codebook with vectors of the form $w_{} = \begin{bmatrix}\sqrt{1 - \gamma_{0}^{2}} \\{\gamma_{0}^{j\; \theta_{}}}\end{bmatrix}$ with a set of uniform phases$\theta_{} = \frac{2\pi \; }{N_{l} - 1}$ for l=0, 1, . . . ,N_(l)−2.
 17. The method of claim 13, wherein the base station has fourtransmit antennas, and wherein the n-th codebook is a ring codebookexpressible as: $S_{2} = {\left\{ {\begin{bmatrix}1 \\0\end{bmatrix},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\1\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\j\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- 1}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\{- j}\end{bmatrix}}} \right\}.}$
 18. The method of claim 13, wherein the basestation has two transmit antennas, and wherein the n-th codebook is aring codebook with vectors of the form $w_{} = \begin{bmatrix}\sqrt{1 - \gamma_{0}^{2}} \\{{\overset{\sim}{w}}_{}\gamma_{0}^{j\; \theta_{}}}\end{bmatrix}$ with a set of uniform phases$\theta_{} = \frac{2\pi \; }{N_{l} - 1}$ for l=0, 1, . . . ,N_(l)−2.
 19. The method of claim 13, wherein the base station has threetransmit antennas, and wherein the n-th codebook is a ring codebookexpressible as: $S_{3} = {{\frac{1}{\sqrt{3}}\begin{Bmatrix}{\begin{bmatrix}3 \\0 \\0\end{bmatrix},\begin{bmatrix}1 \\1 \\1\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\^{{j2\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\^{{j2\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\1\end{bmatrix},} \\{\begin{bmatrix}1 \\1 \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j4\pi}/3} \\^{{j4\pi}/3}\end{bmatrix},\begin{bmatrix}1 \\^{{j2\pi}/3} \\1\end{bmatrix},\begin{bmatrix}1 \\1 \\^{{j2\pi}/3}\end{bmatrix}}\end{Bmatrix}}..}$
 20. The method of claim 13, wherein the base stationhas four transmit antennas, and wherein the n-th codebook is a ringcodebook with ${\gamma_{0} = \frac{\sqrt{3}}{2}},$ the ring codebook isexpressible as: $S_{4} = {{\frac{1}{2}\begin{Bmatrix}{\begin{bmatrix}2 \\0 \\0 \\0\end{bmatrix},\begin{bmatrix}{- j} \\1 \\{- j} \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- j} \\1 \\j \\1\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\j \\{- 1}\end{bmatrix},} \\{\begin{bmatrix}1 \\{- j} \\{- j} \\1\end{bmatrix},\begin{bmatrix}{- 1} \\{- j} \\j \\{- 1}\end{bmatrix},\begin{bmatrix}{- j} \\{- 1} \\{- 1} \\j\end{bmatrix},\begin{bmatrix}j \\1 \\{- 1} \\j\end{bmatrix},} \\{\begin{bmatrix}{- 1} \\{- 1} \\j \\{- j}\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\{- j} \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- j} \\{- j}\end{bmatrix},} \\{\begin{bmatrix}j \\j \\j \\j\end{bmatrix},\begin{bmatrix}1 \\{- 1} \\{- 1} \\1\end{bmatrix},\begin{bmatrix}j \\j \\{- 1} \\{- 1}\end{bmatrix},\begin{bmatrix}{- 1} \\1 \\1 \\{- 1}\end{bmatrix}}\end{Bmatrix}}..}$
 21. The method of claim 1, wherein R is based on amobility of the subscriber unit.
 22. The method of claim 1, wherein theinformation comprises a concatenation of indices of a result of each ofthe R quantizations into their respective codebooks.
 23. The method ofclaim 1, wherein the information comprises a combination of indices of aresult of each of the R quantizations into their respective codebooks.24. The method of claim 1, wherein the information comprises aconcatenation of indices of a result of each of the n-th quantizationsinto their respective codebooks.
 25. The method of claim 1, whereinthere are multiple subscriber units in the wireless communicationssystem, and wherein R is set independently for each subscriber unit. 26.The method of claim 1, wherein the first codebook comprises a localizedcodebook.
 27. The method of claim 1, further comprising prior to thetransmitting the information, applying an error correcting code to theinformation.
 28. The method of claim 1, wherein the first codebook andan n-th codebook are combined in a composite codebook, wherein n isequal to two (2).
 29. A method for base station operation in a wirelesscommunications system, the method comprising: receiving channelinformation from a subscriber unit; extracting R codebook indices fromthe channel information, where R is an integer number; progressivelyreconstructing a channel estimate using the R codebook indices, whereinthe reconstructing starts at a first codebook index and continues to theR-th codebook index, wherein the reconstructing a channel estimate usingan n-th index makes use of an n-th codebook; and outputting thereconstructed channel estimate.
 30. The method of claim 29, wherein theR codebook indices comprises the first codebook index and R−1 refinementindices.
 31. The method of claim 29, wherein the reconstructing thechannel estimate for a first codebook index comprises selecting acodeword from a first codebook corresponding to the first codebookindex.
 32. The method of claim 29, wherein the reconstructing thechannel estimate for an n-th refinement index comprises: scaling an(n−1)-th codebook with the n-th refinement index, thereby producing ann-th codebook, wherein the (n−1)-th codebook is the codebook used in thereconstructing the channel estimate for an (n−1)-th refinement index;selecting a codeword from the n-th codebook corresponding to the n-threfinement index; and applying the selected codeword to the channelestimate reconstructed in the reconstructing the channel estimate forthe (n−1)-th refinement index.
 33. The method of claim 29, wherein thefirst codebook is a base codebook.
 34. The method of claim 33, whereinthe first codebook comprises a Grassmannian codebook, a Kerdockcodebook, a mutually unbiased base codebook, or a vector quantizationderived codebook.
 35. The method of claim 29, wherein an n-th codebookcomprises a localized codebook.
 36. The method of claim 29, wherein theprogressive reconstructing is performed in increasing order of codebookindices, from 1 to R.
 37. The method of claim 29, further comprisingprior to the extracting, performing an error check on the channelinformation.
 38. The method of claim 29, wherein an n-th codebook is asubset of the first codebook.
 39. A base station comprising: a schedulerconfigured to select one or more users for transmission in atransmission opportunity; a beamforming unit coupled to the scheduler,the beamforming unit configured to map information for the selectedusers onto a beamforming vector for transmission; a progressivereconstruction unit configured to reconstruct a channel estimate fromchannel feedback information provided by a subscriber station, whereinthe progressive reconstruction unit progressively creates the channelestimate from a base index to a base codebook and at least onerefinement index to a localized codebook, wherein the base index and therefinement indices are conveyed in the channel feedback information; asingle user unit coupled to the scheduler, to the beamforming unit, andto the progressive reconstruction unit, the single user unit configuredto provide single user beamforming vectors to the beamforming unit,wherein the single user beamforming vectors are generated by the singleuser unit based on the selected users and the channel estimate; and amulti-user unit coupled to the scheduler, to the beamforming unit, andto the progressive reconstruction unit, the multi-user unit configuredto provide multi-user beamforming vectors to the beamforming unit,wherein the multi-user beamforming vectors are generated by themulti-user unit based on the selected users and the channel estimate.40. The base station of claim 39, wherein the progressive reconstructionunit is further configured to perform an error check on the channelfeedback information.
 41. The base station of claim 39, furthercomprising a modulation and coding unit coupled between the schedulerand the beamforming unit, the modulation and coding unit configured toconvert the information from the selected users into transmissionsymbols.
 42. The base station of claim 39, wherein the base codebook andthe localized codebook are stored in a memory.
 43. The base station ofclaim 39, wherein the base codebook and the localized codebook aredownloaded while the base station is in operation.
 44. The base stationof claim 39, further comprising a switching unit coupled to thescheduler, to the progressive reconstruction unit, to the single userunit, and to the multi-user unit, the switching unit configured toselectively couple an output of the progressive reconstruction unit toeither the single user unit or the multi-user unit.
 45. The base stationof claim 39, wherein the channel feedback information comprisesquantized channel state information, progressive quantized channel stateinformation, preferred modulation and coding modes, or Signal toInterference-plus-Noise Ratio (SINR) information.
 46. A subscriberstation comprising: a channel estimate unit coupled to a receiveantenna, the channel estimate unit configured to estimatecharacteristics of a communications channel between the subscriberstation and a base station; a mobility estimate unit coupled to thereceive antenna, the mobility estimate unit configured to compute ameasure of the mobility of the subscriber station; a progressivequantization unit coupled to the channel estimate unit and to themobility estimate unit, the progressive quantization unit configured toprogressively quantize the estimated characteristics of thecommunications channel by quantizing the estimated characteristics witha base codebook, thereby producing a quantized estimatedcharacteristics, and progressively quantizing the quantized estimatedcharacteristics with localized codebooks; and a progressive feedbackunit coupled to the progressive quantization unit, the progressivefeedback unit configured to generate a feedback message from indices ofa result of each of the quantizations into their respective codebooks.47. The subscriber station of claim 46, wherein the progressivequantization unit is further configured to select a number ofquantizations performed by the progressive quantization unit based onthe measure of mobility of the subscriber station.
 48. The subscriberstation of claim 46, further comprising a performance estimate unitcoupled to the receive antenna, the performance estimate unit configureto estimate an indication of performance corresponding to a signalreceived by the receive antenna.
 49. The subscriber station of claim 46,wherein the base codebook and the localized codebook are stored in amemory.
 50. The subscriber station of claim 49, wherein the basecodebook and the localized codebook are downloaded while the basestation is in operation.